Finite Group Databasebeta

← #11792275

Subgroups — #11792275

Order 1152.

833 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 833 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#942C212yesmaximal, complemented
2#10595044C211yesmaximal, characteristic
3#10592928C211yesmaximal, characteristic, complemented
4C2×#63568C212yesmaximal, complemented
5#10589168C211yesmaximal, characteristic, complemented
6#72110—32nomaximal
7C22×C32×Q8C2211yescharacteristic
8C2×C3×#235C2212yes—
9C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
10C2×C4×C3⋊Dic3C2211yescharacteristic
11C2×C3×#216—22no—
12C3×#942—24no—
13C3×#942—24no—
14C2×C3×#215—22no—
15C2×C3×#208C2212yes—
16#63980—22no—
17#63908—22no—
18#63856—22no—
19#63658—22no—
20#63568—24no—
21C2×C3×#137—32no—
22#5833—32no—
23C2×#942D312yescomplemented
24C2×#837—32no—
25#5229—32no—
26#5229—61no—
27C2×#825—32no—
28#4554—32no—
29C2×C32×Q8—21no—
30C2×C32×Q8—22no—
31C2×C32×Q8—22no—
32C2×C32×Q8D412yescomplemented
33C22×C32×C4—21no—
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3—21no—
36C22×C3⋊Dic3D412yes—
37C2×C3×#67—22no—
38C3×#235—22no—
39C3×#235—22no—
40C3×#235—22no—
41C3×#235—22no—
42C2×C3×D12D412yes—
43C2×C3×C4×D3—22no—
44C2×C3×Dic6D412yes—
45C2×#625—22no—
46C4⋊(C3⋊Dic3)—22no—
47C4×C3⋊Dic3—22no—
48C3×#216—28no—
49C3×#215—28no—
50C3×#208—22no—
51C3×#208D414yescomplemented
52C2×C3×C3⋊C8—22no—
53#3724—22no—
54(C2×D3)⋊Dic3—24no—
55#2007—91noSylow
56C2×C3×#41—32no—
57C22×C3×Q8—21no—
58C22×C3×Q8C2×D312yes—
59C2×#235C2×D312yes—
60C3×#137—64no—
61C3×#137—64no—
62C2×C3×Q16—62no—
63C2×C3×SD16—62no—
64C2×C3×M16—32no—
65#946—62no—
66C2×#216—22no—
67#942—24no—
68#942—24no—
69C2×#215—22no—
70#939—64no—
71#938—62no—
72#930—62no—
73C2×C4⋊Dic3—32no—
74C2×C4⋊Dic3—61no—
75#924—62no—
76C2×C4×Dic3—32no—
77C2×C4×Dic3—61no—
78C2×#208C2×D312yes—
79#837—64no—
80C3⋊#95—64no—
81C3⋊#95—64no—
82#825—64no—
83C23×C32C2×D411yescharacteristic
84C22×C3×D3—22no—
85C32×Q8—24no—
86C32×Q8—42no—
87C2×C32×C4—22no—
88C2×C32×C4—41no—
89C2×C32×C4—41no—
90C2×C32×C4C2×D412yes—
91C2×C32×C4C2×D412yes—
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4#4111yescharacteristic
94C2×C3⋊Dic3—22no—
95C2×C3⋊Dic3—22no—
96C2×C3⋊Dic3—41no—
97C2×C3⋊Dic3—41no—
98C2×C3⋊Dic3—42no—
99C3×#67—42no—
100C3×#67—42no—
101C2×C3×Dic3—22no—
102C3×D12—22no—
103C3×D12—22no—
104C3×C4×D3—42no—
105C3×C4×D3—42no—
106C3×Dic6—22no—
107C3×Dic6—22no—
108#625—82no—
109C3×C3⋊C8—24no—
110C2×#137—32no—
111#537—91no—
112C2×#104—92no—
113#391—91no—
114#343—91no—
115C3×#41—62no—
116C3×#41—62no—
117C3×#41—62no—
118C3×#41—62no—
119C2×C3×Q8—22no—
120C2×C3×Q8—22no—
121C2×C3×Q8—22no—
122C2×C3×Q8—22no—
123C2×C3×Q8—22no—
124C2×C3×Q8—22no—
125C2×C3×Q8—22no—
126C2×C3×Q8—32no—
127C2×C3×Q8—42no—
128C2×C3×Q8—42no—
129C2×C3×Q8#6714yescomplemented
130C2×C3×D4—32no—
131C2×C3×D4—62no—
132C22×C3×C4—22no—
133C22×C3×C4—22no—
134C22×C3×C4—21no—
135C22×C3×C4—62no—
136C22×C3×C4C22×D312yes—
137C2×#67—22no—
138C2×#67—64no—
139C22×Dic3—34no—
140C22×Dic3—62no—
141C22×Dic3—62no—
142C22×Dic3—62no—
143#235—22no—
144#235—22no—
145#235—22no—
146#235—22no—
147C2×D12#6712yes—
148C2×C4×D3—22no—
149C2×Dic6#6712yes—
150C3×Q16—68no—
151C3×SD16—68no—
152C3×M16—34no—
153C3×M16—62no—
154C2×C3×C8—62no—
155#217—64no—
156#216—28no—
157#215—28no—
158(C2×D3)⋊C4—64no—
159C4⋊Dic3—62no—
160C4⋊Dic3—62no—
161C4⋊Dic3—122no—
162Dic3⋊C4—64no—
163C4×Dic3—62no—
164C4×Dic3—62no—
165C4×Dic3—122no—
166#208—22no—
167#208#6714yescomplemented
168C2×C3⋊C8—22no—
169C22×C32—21no—
170C22×C32—21no—
171C22×C32#12011yescharacteristic
172C22×C32#12111yescharacteristic
173C22×C32#12711yescharacteristic
174C2×C3×D3—42no—
175C2×C3×D3—42no—
176C2×C3×D3—42no—
177C32×C4—42no—
178C32×C4#12012yes—
179C32×C4#12112yes—
180C3⋊Dic3—42no—
181C3⋊Dic3—42no—
182C3×Dic3—42no—
183C2×#41—32no—
184C22×Q8D3211yescharacteristic
185#137—64no—
186#137—64no—
187C2×Q16—62no—
188C2×SD16—62no—
189C2×M16—32no—
190C22⋊Q8—182no—
191#121—182no—
192#121—182no—
193C2×C4⋊C4—91no—
194C2×C42—91no—
195#104—184no—
196#95—182no—
197C23×C3—21no—
198C23×C3—62no—
199C23×C3D3×D412yes—
200C22×D3—22no—
201C3×Q8—24no—
202C3×Q8—24no—
203C3×Q8—44no—
204C3×Q8—44no—
205C3×Q8—42no—
206C3×Q8—42no—
207C3×Q8—62no—
208C3×Q8—62no—
209C3×D4—62no—
210C3×D4—62no—
211C3×D4—122no—
212C3×D4—122no—
213C2×C3×C4—24no—
214C2×C3×C4—24no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—22no—
218C2×C3×C4—22no—
219C2×C3×C4—42no—
220C2×C3×C4—42no—
221C2×C3×C4—42no—
222C2×C3×C4—42no—
223C2×C3×C4—62no—
224C2×C3×C4—122no—
225C2×C3×C4—122no—
226C2×C3×C4D3×D412yes—
227C2×C3×C4D3×D412yes—
228C2×C3×C4#23712yes—
229C2×C3×C4C2×#6712yes—
230C2×C3×C4C2×#6712yes—
231C2×C3×C4C2×#6712yes—
232#67—42no—
233#67—42no—
234#67—244no—
235C2×Dic3—22no—
236C2×Dic3—64no—
237C2×Dic3—64no—
238C2×Dic3—64no—
239C2×Dic3—122no—
240C2×Dic3—122no—
241C2×Dic3—122no—
242C2×Dic3—122no—
243C2×Dic3—122no—
244C2×Dic3—124no—
245C2×Dic3—124no—
246D12—22no—
247D12—22no—
248C4×D3—42no—
249C4×D3—42no—
250Dic6—22no—
251Dic6—22no—
252C3×C8—64no—
253C3⋊C8—24no—
254C2×C32—21no—
255C2×C32—21no—
256C2×C32#39211yescharacteristic
257C2×C32#45511yescharacteristic
258C2×C32#45611yescharacteristic
259C3×D3—82no—
260#41—62no—
261#41—62no—
262#41—62no—
263#41—62no—
264C2×Q8—21no—
265C2×Q8—22no—
266C2×Q8—22no—
267C2×Q8—32no—
268C2×Q8#62512yescomplemented
269C2×D4—32no—
270C2×D4—62no—
271C2×D4—182no—
272C22×C4—21no—
273C22×C4—62no—
274C22×C4—92no—
275C22×C4—181no—
276C22×C4C2×D3211yescharacteristic
277Q16—68no—
278SD16—68no—
279M16—34no—
280M16—62no—
281C2×C8—62no—
282C4⋊C4—182no—
283C4⋊C4—182no—
284C22⋊C4—184no—
285C42—182no—
286C22×C3—22no—
287C22×C3—22no—
288C22×C3—22no—
289C22×C3—22no—
290C22×C3—21no—
291C22×C3—21no—
292C22×C3—21no—
293C22×C3—122no—
294C22×C3—122no—
295C22×C3—122no—
296C22×C3#93712yes—
297C22×C3#93912yes—
298C22×C3#94012yes—
299C2×D3—42no—
300C2×D3—42no—
301C2×D3—42no—
302C3×C4—22no—
303C3×C4—22no—
304C3×C4—44no—
305C3×C4—44no—
306C3×C4—122no—
307C3×C4#93712yes—
308C3×C4#93812yes—
309C3×C4#93912yes—
310C3×C4#95312yes—
311Dic3—42no—
312Dic3—124no—
313Dic3—124no—
314Dic3—124no—
315Dic3—242no—
316C32#200711yescharacteristic, complemented, Sylow
317C23—62no—
318C23#381111yescharacteristic
319Q8—24no—
320Q8—42no—
321Q8—62no—
322Q8—62no—
323D4—62no—
324D4—62no—
325D4—122no—
326D4—122no—
327D4—722no—
328C2×C4—22no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—62no—
332C2×C4—122no—
333C2×C4—122no—
334C2×C4—182no—
335C2×C4—182no—
336C2×C4—361no—
337C2×C4—361no—
338C2×C4—362no—
339C2×C4#380511yescharacteristic
340C2×C4C2×#62511yescharacteristic
341C2×C4D3×#6712yes—
342C2×C4D3×#6712yes—
343C8—64no—
344C2×C3—22no—
345C2×C3—22no—
346C2×C3—22no—
347C2×C3—22no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—21no—
351C2×C3—242no—
352C2×C3#520212yes—
353C2×C3#520512yes—
354C2×C3#522312yes—
355D3—82no—
356C22—21no—
357C22—21no—
358C22—122no—
359C22—122no—
360C22—122no—
361C22#6397911yescharacteristic
362C22#6398011yescharacteristic
363C22#6398311yescharacteristic
364C4—42no—
365C4—122no—
366C4—362no—
367C4—362no—
368C4#6397012yes—
369C4#6397612yes—
370C3—21no—
371C3#7211012yescomplemented
372C2—21no—
373C2—21no—
374C2—242no—
375C2#1059165811yescharacteristic
376C2#1059166011yescharacteristic
377C2#1059172311yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC22×C32#120
prime radical#10595044C2
hypercenterC22×Q8D32
hypocenterC32#2007
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C3×#942C2semidirect
3. #10592928C2semidirect
4. C2×#63568C2semidirect
5. #10589168C2semidirect
23. C2×#942D3semidirect
32. C2×C32×Q8D4semidirect
51. C3×#208D4semidirect
129. C2×C3×Q8#67semidirect
167. #208#67semidirect
268. C2×Q8#625semidirect
316. C32#2007semidirect
371. C3#72110semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C3×#9422
#105950442
#105929282
C2×#635682
#105891682
#721103